If 6x-y-36 and 3x-y-729- then x2-y2-

Given: #160;6x y=36and #160;3x+y=729 #160;6x y=36 #8658; #160;6x y=62 #8658;x y=2 #160; #160; #160; #160; #160; #160; #160; #160; ...

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Standard VII

Mathematics

Types of Brackets

If 6x-y=36 an...

Question

If 6^x–y = 36 and 3^x+y= 729, then x² – y² = _________.

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Solution

$Given : 6^{x - y} = 36 and 3^{x + y} = 729 6^{x - y} = 36 \Rightarrow 6^{x - y} = 6^{2} \Rightarrow x - y = 2 . . . (1) 3^{x + y} = 729 \Rightarrow 3^{x + y} = 3^{6} \Rightarrow x + y = 6 . . . (2) Adding (1) and (2), we get 2 x = 8 \Rightarrow x = 4 Substituting the value of x in (2), we get 4 + y = 6 \Rightarrow y = 2 Now, x^{2} - y^{2} = 4^{2} - 2^{2} = 16 - 4 = 12$

Hence, x² – y² = 12.

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If 6x–y = 36 and 3x+y = 729, then x2 – y2 = _________.

Given: 6x-y=36and 3x+y=729 6x-y=36⇒ 6x-y=62⇒x-y=2 ...13x+y=729⇒3x+y=36⇒x+y=6 ...2Adding 1 and 2, we get2x=8⇒x=4Substituting the value of x in 2, we get4+y=6⇒y=2Now,x2-y2=42-22 =16-4 =12 Hence, x2 – y2 = 12.

If 6^x–y = 36 and 3^x+y= 729, then x² – y² = _________.